Is 900 a Prime Number?

There are two types of numbers, mostly — Prime numbers and composite numbers, depending on the number of factors. A prime number is a natural number that is divisible only by 1 and itself. For example, 3 is a prime number because it is divisible by 1 and itself.

A composite number is a positive number that is divisible by more than two numbers. For example, 6 is divisible by 1, 2, 3, and 6, making it a composite number.

Prime numbers follow a few properties like: -

• Prime numbers are positive numbers always greater than 1. 
• 2 is the only even prime number. 
• They have only two factors: 1 and the number itself. 
• Any two distinct prime numbers are co-prime numbers because they have only one common factor, which is 1.
• As 900 has more than two factors, it is not a prime number.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 900 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. These methods include: -

1. Counting Divisors Method 
2. Divisibility Test 
3. Prime Number Chart 
4. Prime Factorization

The method in which we count the number of divisors to categorize the numbers as prime or composite is called the counting divisors method. Based on the count of the divisors, we categorize prime and composite numbers. -

• If there is a total count of only 2 divisors, then the number would be prime. 
• If the count is more than 2, then the number is composite.

Let’s check whether 900 is prime or composite.

Step 1: All numbers are divisible by 1 and itself.

Step 2: Divide 900 by 2. It is divisible by 2, so 2 is a factor of 900.

Step 3: Divide 900 by 3. It is divisible by 3, so 3 is a factor of 900.

Step 4: You can simplify checking divisors up to 900 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 900 by 2, 3, 5, and other numbers, it is divisible by many including 2, 3, 5, and 10.

Since 900 has more than 2 divisors, it is a composite number.

We use a set of rules to check whether a number is divisible by another number completely or not. This is called the Divisibility Test Method. 

Divisibility by 2: The number in the ones' place value is 0, which means that 900 is divisible by 2. 

Divisibility by 3: The sum of the digits in the number 900 is 9. Since 9 is divisible by 3, 900 is divisible by 3. 

Divisibility by 5: The unit’s place digit is 0. Therefore, 900 is divisible by 5. 

Divisibility by 7: Check divisibility by performing the specific test for 7. Since it doesn't divide exactly, 900 is not divisible by 7. 

Divisibility by 11: In 900, the sum of the digits in odd positions is 9, and the sum of the digits in even positions is 0. The difference is 9, which means 900 is not divisible by 11.

Since 900 is divisible by more than two numbers, it is a composite number.

The prime number chart is a tool created by using a method called “The Sieve of Eratosthenes.” In this method, we follow these steps:

Step 1: Write numbers from 1 to 1000 in rows and columns.

Step 2: Leave 1 without coloring or crossing, as it is neither prime nor composite.

Step 3: Mark 2 because it is a prime number and cross out all the multiples of 2.

Step 4: Mark 3 because it is a prime number and cross out all the multiples of 3.

Step 5: Repeat this process until you reach the table consisting of marked and crossed boxes, except 1. Through this process, we will have a list of prime numbers.

Since 900 is not present in the list of prime numbers, it is a composite number.

Prime factorization is a process of breaking down a number into prime factors and then multiplying those factors to obtain the original number.

Step 1: We can write 900 as 9 × 100.

Step 2: Break down 9 into 3 × 3 and 100 into 10 × 10.

Step 3: Further break down 10 into 2 × 5. Step 4: Now we get the product consisting of only prime numbers.

Hence, the prime factorization of 900 is 2 × 2 × 3 × 3 × 5 × 5.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 12 is a composite number because 12 is divisible by 1, 2, 3, 4, 6, and 12.

• Prime factorization: A method of expressing a number as the product of its prime factors.

• Divisibility rules: Rules that help determine whether a number is divisible by another without performing full division.

• Perfect square: A number that can be expressed as the square of an integer. For example, 16 is a perfect square because it is 4 squared.

• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.